A Generalized Approach to Heat Transfer in Pipe Flow with Internal Heat Generation

In the last few years, there has been a renewed interest in the Molten Salt Reactor (MSR), one of the "Generation IV International Forum" concepts, which adopts a circulating molten salt mixture as both heat generator (fuel) and coolant. The heat transfer of a fluid with internal heat generation depends on the strength of the source whose influence on the heat exchange process is significant enough to demand consideration. At present, few studies have been performed on the subject from either an experimental or a numerical point of view. This study considers fluids with a wide range of Reynolds numbers, flowing through smooth and straight circular tubes within which the flow is hydrodynamically developed but thermally developing (conditions of interest for MSR core channels). The study aims at an assessment of the heat transfer modelling for a large variety of fluids (with Prandtl numbers in the range 0 ≤ Pr ≤ 10^4), in particular taking into account the influence of the internal heat generation on the temperature distribution, which plays an important role in the case of molten salts for nuclear reactors. To this purpose, the general and unified solution of the heat transfer equation is applied to the turbulent Graetz problem with boundary conditions of the third kind and arbitrary heat source distribution, incorporating recent formulations for turbulent flow and convection. Computed results are shown to be in a good agreement with experimental data concerning heat transfer evaluations for both fully developed and thermally developing flow conditions, over a large range of Prandtl numbers (10^-2 < Pr < 10^4). Finally, a preliminary correlation, which includes the Prandtl number range of interest for molten salts, is proposed for the Nusselt number predictions in the case of simultaneous uniform wall heat flux and internal heat generation.